Related papers: Solving Random Satisfiability Problems with Quantu…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…
Operating on the principles of quantum mechanics, quantum algorithms hold the promise for solving problems that are beyond the reach of the best-available classical algorithms. An integral part of realizing such speedup is the…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantum computation increases by decreasing…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
Quantum computers can solve specific problems that are not feasible on "classical" hardware. Harvesting the speed-up provided by quantum computers therefore has the potential to change any industry which uses computation, including finance.…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of…
Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…